Найдите корень уравнения:
1)

x - \frac{7 x + 1}{8} = \frac{4 x + 3}{4}

;
2)

\frac{2 x + 1}{6} - \frac{3 x + 1}{7} = 2

;
3)

\frac{2 x + 3}{3} - \frac{5 x + 13}{6} + \frac{5 - 2 x}{2} = 6

;
4)

\frac{4 x^{2} + 5 x}{14} + \frac{10 - 2 x^{2}}{7} = 5

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Алгебре 7 класс Мерзляк. Номер №376

x - \frac{7 x + 1}{8} = \frac{4 x + 3}{4}

x - \frac{7 x + 1}{8} - \frac{4 x + 3}{4} = 0

\frac{8 x - 7 x - 1 - 2 (4 x + 3)}{8} = 0

\frac{8 x - 7 x - 1 - 8 x - 6}{8} = 0

8x − 7x − 1 − 8x − 6 = 0
−7x = 6 + 1
x = 7 : (−7)
x = −1

\frac{2 x + 1}{6} - \frac{3 x + 1}{7} = 2

\frac{7 (2 x + 1) - 6 (3 x + 1)}{42} = 2

7(2x + 1) − 6(3x + 1) = 2 * 42
14x + 7 − 18x − 6 = 84
−4x = 84 − 7 + 6
−4x = 83

x = - \frac{83}{4}

x = - 20 \frac{3}{4}

x = −20,75

\frac{2 x + 3}{3} - \frac{5 x + 13}{6} + \frac{5 - 2 x}{2} = 6

\frac{2 (2 x + 3) - (5 x + 13) + 3 (5 - 2 x)}{6} = 6

2(2x + 3) − (5x + 13) + 3(5 − 2x) = 6 * 6
4x + 6 − 5x − 13 + 15 − 6x = 36
4x − 5x − 6x = 36 − 6 + 13 − 15
−7x = 28
x = 28 : −7
x = −4

\frac{4 x^{2} + 5 x}{14} + \frac{10 - 2 x^{2}}{7} = 5

\frac{4 x^{2} + 5 x + 2 (10 - 2 x^{2})}{14} = 5

4 x^{2} + 5 x + 2 (10 - 2 x^{2}) = 5 * 14

4 x^{2} + 5 x + 20 - 4 x^{2} = 70

5x = 70 − 20
x = 50 : 5
x = 10

ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир